Here is one way to write the same letter three times: n + n + n. Is there a neater way to write three of the same letter added together?
Take three hands-up answers, not open call-outs. Listen for a pupil who offers 3n — revoice it, but don't confirm the rule yet; that lands in Watch and Notice.
Think of each x as a bag with an unknown number of cubes inside, and each plain number as loose cubes on the table. Watch three expressions get tidied up on the board. Before each answer appears, predict which cards match and can be pushed together, and which have to stay apart. Then we check.
In the second, a lone loose number had nothing to join. In this last one, be ready to say what the two loose numbers, 5 and 1, make when they join.
Work the three expressions on the board, grouping like terms as the class predicts. Between the three expressions, turn-and-name a pupil to say the group before you reveal each answer, so the beat keeps moving.
Sort the scattered cards into two groups. Put the x-bags (the x-terms) in one place. Put the loose cubes (the plain numbers) in the other. The cards on screen are 5x, 2, 3x, x and 4. When they are sorted, say the simplified expression aloud.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.
Use counters or cube-and-bag cards at pupils' desks so everyone sorts as the board is sorted. Watch for a pupil who tries to slide a loose number into the x-bag pile — that is the misconception to surface. Can a plain 4 ever hide inside a bag we can't count?
The x-terms are 5x + 3x + x, which make 9x; the loose cubes are 2 + 4, which make 6. Once the cards are grouped (9x in the x-bags, 6 in the loose cubes), lead the class to state the simplified expression as 9x + 6.
In your maths copy, simplify each of these expressions by collecting like terms. Before you combine anything, underline the like terms in matching colours — all the x-terms one colour, all the plain numbers another.
Write the simplified expression at the end of each line.
Walk the room glancing at the colour underlining before pupils combine — this is whole-class copybook practice, not marking. Catch anyone who writes a single term like 6x from 4x + 3 + 2x; the loose 3 must survive.
Sort the scattered terms into the right groups, then write the simplified expression underneath. The sets get harder as you go. The first has two x-terms and one number. The next has two x-terms with two numbers. The later ones mix three x-terms with two numbers. Predict how many x-bags and how many loose cubes each set will end with before you check.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
After each Check, ask the class to state the simplified expression in full (both groups), so the answer is 7x + 3, not just 7x.
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